Routing methods for quantum communication paths across a mesh quantum network

ABSTRACT

A method for routing in a quantum network is provided. The method may include receiving parameters including a fidelity with coherence decay time and an entanglement generation rate for each quantum node in a mesh quantum network by a controller, the controller being configured to communicate with each quantum node of a plurality of quantum nodes in the mesh quantum network. Each quantum node includes a quantum memory and a processor. The method may also include analyzing the fidelity with coherence decay time and the entanglement generation rate to yield a determination of a path fidelity with a path coherence decay time and a path entanglement generation rate between at least one pair of quantum nodes. The method may further include, based on the determination, selecting a quantum communication path from a source node to a destination node.

FIELD

The disclosure is directed to routing methods or routing algorithms inquantum teleporting in a quantum network.

BACKGROUND

The development of quantum computing creates new requirements toimplement a quantum network, which is also known as a quantum internet.The implementation for the quantum network is very different from thatof a traditional classical network, because the quantum computing willrequire transfer of qubits. There are two models aimed for qubittransmission. One model is based on teleporting using quantum entangledBell States, and another model permits direct transmission using quantumerror correction. Teleporting is a technique for transferring quantuminformation from a sender at one location to a receiver at anotherremote location using a pair of entangled quantum particles. Both modelsare indeed technique to send the quantum information from the sender tothe receiver. Both models assume the possible use of quantum repeatersto extend the distance between the sender and the receiver. The use ofthe models may depend on a total distance, a repeater distance, and thetechnology applied. It is well understood that in nodes where therepeater is implemented, a quantum channel can be routed or switched toa proper destination.

BRIEF SUMMARY

In one aspect, a method for routing in a quantum network is provided.The method may include receiving parameters including a fidelity withcoherence decay time and an entanglement generation rate for eachquantum node in a mesh quantum network by a controller, the controllerbeing configured to communicate with each quantum node of a plurality ofquantum nodes in the mesh quantum network, each quantum node including aquantum memory and a processor, for example, a classical processor. Themethod may also include analyzing the fidelity with coherence decay timeand the entanglement generation rate to yield a determination of a pathfidelity with a path coherence decay time and a path entanglementgeneration rate between at least one pair of quantum nodes. The methodmay further include, based on the determination, selecting, through themesh quantum network, a quantum communication path from a first endpoint or a source node to a second end point or a destination node.

In another aspect, a controller may include one or more processors, anda non-transitory computer readable medium including instructions storedtherein. The instructions, when executed by the one or more processors,cause the processors perform operations including receiving parametersincluding a fidelity with coherence decay time and an entanglementgeneration rate for each quantum node in a mesh quantum network, thecontroller being configured to communicate with each quantum node of aplurality of quantum nodes in the mesh quantum network, each quantumnode including a quantum memory and a processor. The instructions, whenexecuted by the one or more processors, also cause the processorsperform operations including analyzing the fidelity with coherence decaytime and the entanglement generation rate to yield a determination of apath fidelity with a path coherence decay time and a path entanglementgeneration rate between at least one pair of quantum nodes. Theinstructions, when executed by the one or more processors, also causethe processors perform operations including, based on the determination,selecting, through the mesh quantum network, a quantum communicationpath from a first end point or a source node to a second end point or adestination node.

In a further aspect, a non-transitory computer readable medium mayinclude instructions. The instructions, when executed by a computingsystem, cause the computing system to perform operations includingreceiving parameters including a fidelity with coherence decay time andan entanglement generation rate for each quantum node in a mesh quantumnetwork, the controller being configured to communicate with eachquantum node of a plurality of quantum nodes in the mesh quantumnetwork, each quantum node including a quantum memory and a processor.The instructions, when executed by the computing system, also cause theprocessors perform operations including analyzing the fidelity withcoherence decay time and the entanglement generation rate to yield adetermination of a path fidelity with a path coherence decay time and apath entanglement generation rate between at least one pair of quantumnodes. The instructions, when executed by the computing system, alsocause the processors perform operations including, based on thedetermination, selecting, through the mesh quantum network, a quantumcommunication path from a first end point or a source node to a secondend point or a destination node.

Additional embodiments and features are set forth in part in thedescription that follows, and will become apparent to those skilled inthe art upon examination of the specification or may be learned by thepractice of the disclosed subject matter. A further understanding of thenature and advantages of the disclosure may be realized by reference tothe remaining portions of the specification and the drawings, whichforms a part of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The description will be more fully understood with reference to thefollowing figures and data graphs, which are presented as variousembodiments of the disclosure and should not be construed as a completerecitation of the scope of the disclosure, wherein:

FIG. 1A is a network system diagram including a controller, inaccordance with some aspects of the disclosed technology;

FIG. 1B is a diagram of the node of FIG. 1A, in accordance with someaspects of the disclosed technology;

FIG. 2A illustrates a qubit to transmit and a two Bell state entangledpair of particles before teleporting, in accordance with some aspects ofthe disclosed technology;

FIG. 2B illustrates a bell state measurement (BSM) between the qubit totransmit and one of the two Bell state entangled pair, in accordancewith some aspects of the disclosed technology;

FIG. 2C illustrates a transmission of a BSM result via 2 bits on aclassical channel, in accordance with some aspects of the disclosedtechnology;

FIG. 2D illustrates performing an unitary operation defined by the BSMresult to recover a teleported qubit, in accordance with some aspects ofthe disclosed technology;

FIG. 3A illustrates an entanglement swapping starting from multiplepairs of entangled particles, in accordance with some aspects of thedisclosed technology;

FIG. 3B illustrates that the entanglement swapping is performed via aBSM on particles in the same node of two different entangled pairpreviously created, in accordance with some aspects of the disclosedtechnology;

FIG. 3C illustrates that teleporting can be achieved by multipleentanglement swapping to form an end-to-end entangled pair, inaccordance with some aspects of the disclosed technology;

FIG. 4 illustrates a mesh quantum network with multiple entangledswapping paths from one end point to reach the same destination oranother end point, in accordance with some aspects of the disclosedtechnology;

FIG. 5 illustrates that an entanglement swapping path can be selected byperforming a BSM operation between each of entangled pairs to identifyan appropriate entanglement swapping path, in accordance with someaspects of the disclosed technology;

FIG. 6 illustrates selecting a path across a mesh quantum network, inaccordance with some aspects of the disclosed technology;

FIG. 7 illustrates splitting a quantum path across a mesh quantumnetwork, in accordance with some aspects of the disclosed technology;

FIG. 8 illustrates a combination of a classical communication path and aquantum communication path, in accordance with some aspects of thedisclosed technology;

FIG. 9 is a flow chart illustrating steps for selecting a routing pathin a quantum network, in accordance with some aspects of the disclosedtechnology; and

FIG. 10 shows an example of computing system, in accordance with someaspects of the disclosed technology.

DETAILED DESCRIPTION

The disclosure may be understood by reference to the following detaileddescription, taken in conjunction with the drawings as described below.It is noted that, for purposes of illustrative clarity, certain elementsin various drawings may not be drawn to scale.

Many routing protocols have been implemented in classical networking butnone of the protocols have constrains like the ones of quantumnetworking technology. Efforts have been made on developing new quantumnetworking protocols. However, the efforts do not focus on how toresolve the path through the quantum network based on the specificconstrains of the quantum networking technology.

In a mesh quantum network, such as the ones that may be implemented in aquantum data center, a quantum campus, or a quantum regional areanetwork, a protocol is required such that quantum computers can ask fora quantum channel in order to communicate quantum information. Thequantum network, also referred to as a quantum internet, is aninterconnection of quantum processors and repeaters that can generate,exchange, and process quantum information. The quantum networkfacilitates the transmission of information in the form of quantum bits,also referred to qubits, between physically separated quantum memories.The quantum channel is a physical media, such as optical fiber channel.

The quantum network might utilize a long distance quantum entanglementof entangled particles between two remote communication parties. Thequantum network can provide security for communications between the tworemote communication parties in that any attempt to hack the systemwould result in a collapse of the quantum state of a respective quantumentangled particle, thus revealing the attempt to hack into acommunication. Applications of the quantum network can be implementedwith many qubits representing quantum information.

To generate the long distance quantum entanglement between two endpoints or two parties through an optical fiber channel, e.g. Alice andBob, one of the end points may create an entangled pair of photons andsend one photon to the other end point. However, the optical fiber islossy such that the success rate of establishing an entanglement pairdecays exponentially with the physical distance between the two endpoints. To increase the success rate of long distance entanglement, anumber of quantum repeaters can be deployed between the two end pointsor parties. The quantum repeaters work entirely different from classicalnetwork routers. To enable long distance entanglement, quantum repeatersuse entanglement swapping. The purpose of entanglement swapping is toessentially position a pair of entangled quantum particles farther apartthan might be possible, due to losses, by physical transmitting one ofthe quantum particles of the pair of quantum particles to a desiredendpoint.

The disclosure is directed to routing methods and protocols thatcomputers or classical computers select an appropriate path for thequantum channel across the mesh quantum network. Before a quantuminformation can be transmitted, each segment or quantum link between twoneighboring nodes needs to have an entangled Bell State to offer inorder to build the path via quantum entangled Bell States. The classicalcomputer can trigger an appropriate entanglement swapping. The quantumnetwork can become an important application that can boost quantumcomputing. The quantum network can rely on quantum regenerators that arebased on quantum memories.

FIG. 1A is a network system diagram including a controller, inaccordance with some aspects of the disclosed technology. As shown, aquantum communication network 100 includes nodes 101A to 101G. Each nodeis connected to at least one other node. In the network 100,communication takes place between a source node or an end node and adestination node or an end node. Intermediate nodes between the sourcenode and the destination node act as repeater nodes. The end nodes arealso referred to as end points.

In the quantum communication network, such as the one illustrated inFIG. 1A, communication between two nodes takes place through a channel106. The channel 106 may be implemented in an optical fiber connection.The channels or links are shown as dash lines between nodes in FIG. 1A.

A controller 108 is in a communication with each node 101 of the network100. The controller 108 may include one or more processors that areconfigured to execute a routing algorithm method for a quantumcommunication path across the network 100. For example, the controller108 can evaluate parameters of each quantum node, e.g. a fidelity withcoherence decay time and entanglement generation rate, and select arouting path through the network 100. More details will be providedlater about the parameters and evaluations. The controller 108 mayinclude a memory device. The routing algorithm includes instructionsthat can be stored in the memory device and executed by the processors.

The quantum communication path via teleporting requires the quantumnetwork to establish an entanglement between two quantum memoriesthrough one or more quantum links.

A quantum channel connects two quantum devices or quantum processors andsupports the transmission of qubits. If a quantum entanglement issuccessful, the link becomes a quantum link or the quantum channel, thenthe two quantum processors share a quantum entanglement pair. Eachquantum https://en.wikipedia.org/wiki/Central_processing_unitprocessoris a small quantum computer being able to perform quantum logic gates ona certain number of qubits.

The quantum repeaters are used as relays to connect quantum processors.However, the quantum repeaters cannot be the source or destination ofany qubit transmission, but can only perform quantum swapping acrossmultiple repeaters, which is also referred to entanglement swapping. Thequantum swapping establishes a long distance quantum entanglement. Thequantum repeater generates an entanglement pair with Alice andsimultaneously generates another entanglement pair with Bob.Entanglement swapping creates long distance entanglement that can beused for teleporting. Teleporting is performed after completing a BSM.Teleporting transfers the qubit or quantum information. In other words,the BSM is used for entanglement generation and entanglement swapping.Once the entangled particles are positioned at the source anddestination nodes, the teleporting that transfers the qubit can occurindependently of any link or path used in the process of positioning theentangled particles. The teleporting process destroys the entangled pairbut transfers the qubit.

In some quantum nodes such as repeaters, there are no source orgenerators of particles. In other words, there are no transmitters inthese quantum repeaters. The particles are transmitted to these quantumrepeaters, such as photons through optical fiber channels.

For the long distance quantum swapping, all nodes on the quantumcommunication path need entangle different particle/memories with itspredecessor and successor simultaneously.

FIG. 1B is a diagram of the source node 101A and/or destination node101G of FIG. 1A, in accordance with some aspects of the disclosedtechnology. As shown in FIG. 1B, node 101A or 101G in the quantumcommunication network 100 may contain a processor 105 in a communicationwith the controller 108 to implement the routing protocol. The processor105 may be a central processing unit (CPU), or graphical processing unit(GPU). The processor 105 is used for path selection and for controllingthe quantum network. The processor 105 is a classical processor which isdifferent from the quantum processor. The quantum processor is a smallquantum computer being able to perform quantum logic gates on a certainnumber of qubits. The node 101A or 101G may also include a quantummemory 107 in a communication with the processor 105.

The node 101A or 101G may also include a quantum communication unit 103in a communication with the processor 105. The quantum communicationunit 103 may include a quantum transmitter 111 and/or a quantum receiver113. In some variations, the quantum transmitter 111 may include asource of the photons, or a qubit generator. In the quantumcommunication network, the quantum transmitter can be capable ofencoding information on photons. The quantum states can be transportedin single qubits/photons or encoded in multiple qubits/photons. Thequantum receiver 113 can be capable of decoding this information. Eitherdiscrete variable (DV) or continuous variable (CV) quantum informationcan be encoded.

In some variations, when one node 101A or 101G is connected to two othernodes, the node 101A or 101G has a quantum communication unit 103 ateach end of the connection to the two other nodes. Thus, every node mayhave a number of quantum communication units 103 that equals to thenumber of connections at the node.

The nodes (e.g. 101B, 101C, 101D, 101E, 101F) may also include abell-state measurement (BSM) station 109 for performing BSM operation.The BSM station 109 is in a communication with the processor 105 andalso in a communication with the quantum memory 107. The Bell states arefour specific two-qubit states, also referred to as four maximallyentangled two-qubit Bell states, which form a maximally entangled basis,known as the Bell basis. Using a quantomechanical notation, the Bellstates are identified as follows:

$\left. \left. {\left. {\left. {\left. {\left. {❘\Phi^{+}} \right\rangle = {\frac{1}{\sqrt{2}}\left( {❘0} \right.}} \right\rangle_{A} \otimes {❘0}} \right\rangle_{B} + {❘1}} \right\rangle_{A} \otimes {❘1}} \right\rangle_{B} \right)$$\left. \left. {\left. {\left. {\left. {\left. {❘\Phi^{-}} \right\rangle = {\frac{1}{\sqrt{2}}\left( {❘0} \right.}} \right\rangle_{A} \otimes {❘0}} \right\rangle_{B} - {❘1}} \right\rangle_{A} \otimes {❘1}} \right\rangle_{B} \right)$$\left. \left. {\left. {\left. {\left. {\left. {❘\Psi^{+}} \right\rangle = {\frac{1}{\sqrt{2}}\left( {❘0} \right.}} \right\rangle_{A} \otimes {❘1}} \right\rangle_{B} + {❘1}} \right\rangle_{A} \otimes {❘0}} \right\rangle_{B} \right)$$\left. \left. {\left. {\left. {\left. {\left. {❘\Psi^{-}} \right\rangle = {\frac{1}{\sqrt{2}}\left( {❘0} \right.}} \right\rangle_{A} \otimes {❘1}} \right\rangle_{B} - {❘1}} \right\rangle_{A} \otimes {❘0}} \right\rangle_{B} \right)$

In the Bell states, the qubit is an equal coherent superposition ofbasis states. An important distinguishing feature between qubits andclassical bits is that multiple qubits can exhibit quantum entanglement.

Quantum teleportation is a technique for transferring quantuminformation from a sender or a source node 101A at one location to areceiver or a destination node 101G at a remote location. The quantumcommunication path is created by implementing entanglement swapping ineach node of the network along a path in order to offer to two endpoints an entangled pair of parties to implement teleporting. Both theentanglement swapping and the teleporting are implemented by executing aBSM operation plus a local operation (e.g. unitary operation) based onthe BSM's outcome and communication via a classical channel on the otherqubit. The BSM operation is performed between two qubits. In case ofentanglement swapping, the two qubits are part of two differententanglement pairs of particles. In case of teleporting, one qubit ispart of an entanglement pair and the other qubit is the one to teleport.After completing quantum swapping, which extends a distance of the firstquantum communication path using entanglement swapping repeaters fromthe source node to the destination node, teleporting transfers quantuminformation based upon the entangled pair of particles in the sourcenode and the destination node.

The steps used for quantum teleporting of a quantum state via a Bellstate entangled pair are illustrated in FIGS. 2A-2D. As shown in FIG.2A, a qubit to transmit 202 and a two Bell state entangled pair 204 ofparticles are illustrated before teleporting. As shown in FIG. 2B, a BSMoperation 206 is performed between the qubit to transmit 202 and oneparticle 204A of an entangled pair, which includes particle 204A andparticle 204B, corresponding to two bits in a classical channel 210. Asshown in FIG. 2C, teleporting occurs through a Bell state entangled pair204 to have a transmission of the BSM result via 2 bits on a classicalchannel 210. As shown in FIG. 2D, a unitary operation 212 defined by theBSM result is performed to recover a teleported qubit 208.

Similarly, FIGS. 3A-3C show how an entanglement swapping extends thedistance between entangled particles (e.g. photons), thus enablingteleportation and communication across multiple hops from one node toanother node.

FIG. 3A illustrates an entanglement swapping starting from multiplepairs of entangled particles, in accordance with some aspects of thedisclosed technology. As shown in FIG. 3A, the transmitters 112 of thecommunication units 103 create a first entangled pair A of particles, asecond entangled pair B of particles, and a third entangled pair C ofparticles. One of the first entangled pair A of particles 301A is at afirst end point 302A which is a quantum node. Also, one of the firstentangled pair A of particles 301B and one of the second entangled pairB of particles 301C are at a first quantum node 302B. Also, one of thesecond entangled pair B of particles 301D and one of the third entangledpair C of particles 301E are at a second quantum node 302C. Further, oneof the third entangled pair of particles 301F is at a second end point302D which is also a quantum node at a remote location from the firstend point 302A.

FIG. 3B illustrates that the entanglement swapping is performed via aBSM on particles in the same node of two different entangled pairpreviously created, in accordance with some aspects of the disclosedtechnology. As shown in FIG. 3B, the BSM station 109 may execute a firstbell state measurement (BSM) operation 304A on one of the firstentangled pair A of particles and one of the second entangled pair B ofparticles at the first quantum node 302B.

The teleporting may include routing the quantum communication path byusing the controller 108, and performing entanglement swapping to form afourth entangled pair D of particles that links the first end point 302Ato the second quantum node 302C, as shown in FIG. 3B.

FIG. 3C illustrates that teleporting can be achieved by multipleentanglement swapping to form an end-to-end entangled pair, inaccordance with some aspects of the disclosed technology. The BSMstation 109 may also execute a second BSM operation 304B on one of thethird entangled pair C of particles and one of the second entangled pairB of particles at the second quantum node 302C, as shown in FIG. 3C. Allthe entanglement swapping needs to be completed before teleporting.However, all the entanglement swapping does not need to be performedsimultaneously or in sequence. One or more quantum links that combine toyield a quantum communication path through the quantum mesh network canbe built or combined in any order or sequence. The teleporting mayinclude routing the quantum communication path or entanglement swappingpath by using the controller, and performing entanglement swapping toform a fifth entangled pair E of particles that links the first endpoint 302A to the second end point 302D, as shown in FIG. 3C.

FIG. 4 illustrates a mesh quantum network with multiple entangledswapping paths from one end point to reach the same destination oranother end point, in accordance with some aspects of the disclosedtechnology. As shown, a mesh quantum network 400 includes a plurality ofquantum nodes 101A-G, and links 404 connecting the plurality of quantumnodes 101A-G. For example, the link 404 connects two neighboring nodes,e.g. nodes 101A and 101B. Each quantum node may include a processor 105in a communication with the controller 108. The network 400 may includedifferent paths 406A and 406B between first and second end points 101Aand 101G. One of the quantum nodes acts as the first end point 101A orsource node. Another quantum node acts as the second end point 101G ordestination node. A shorter path 406A hops from node 101A to node 101Eand then to node 101G, and includes two links 404. A longer path 406Bhops from node 101A to node 101D, then hops to node 101E, then to node101C, and finally hops to node 101G. The longer path includes four links404.

In some variations, one or more quantum nodes may be repeaters.

In some variations, the particles may include photons. The quantumchannel may include an optical fiber cable transmitting qubits carriedby the photons.

FIG. 5 illustrates that an entanglement swapping path can be selected byperforming a BSM operation between each of entangled pairs to identifyan appropriate entanglement swapping path, in accordance with someaspects of the disclosed technology. As shown in FIG. 5 , there are fiveentangled pairs 502A-E with one of each of five entangled pairs in anode 506. A BSM matrix 504 includes BSM operations for each of theentangled pairs 502A-E for the node 506. The BSM operations can beperformed on the five entangled pairs to determine which pair becomesthe appropriate entanglement swapping path that includes the node 506.For example, the node 506 may represent node 101E as shown in FIG. 4 ,which may have five entangled pairs to nodes 101A, 101B, 101C, 101D, and101G as shown in FIG. 4 . Note that not all nodes in the network can beentangled, such as node 101F. The node 502B may represent a source node101A which connects to one party, e.g. Alice. The node 502D mayrepresent a destination node which connects to another party, e.g. Bob.

Independently of the technology implemented to generate the Bell stateentangled pair suitable for entanglement swapping and teleporting, thequantum state needs to be stored into a quantum memory. It is well knownthat storing the quantum state is a very sensitive operation, becausethe quantum state may change over time due to the quantum memory'sinteraction with the environment. Such a phenomena is calleddecoherence. The quantum memory has a decoherence time, which is alsoreferred to as a coherence decay time.

Four parameters are normally used to describe quantum links and quantumrepeaters, including generation rate of Bell state, multiplexing orstoring capacity, fidelity, and lifetime or decoherence time. While thegeneration rate and storing capacity may be similar to the bandwidthcapacity of a classical channel, there is no equivalent for fidelity andlifetime. The fidelity is a parameter that characterizes quality of theentangled pairs offered for the communication. The fidelity drops withtime according to the decoherence time that is characteristic of thespecific quantum memory technology. The fidelity also drops similarlywith the number of quantum operations, including entanglement swapping,as a function of quantum gate technology. The fidelity may be improvedconsuming multiple parallel entangled Bell states on the same link. Suchan operation is known as entanglement purification.

Two important parameters, i.e. fidelity (dropping with the coherencetime), and entanglement generation rate, are identified to build anappropriate protocol that implements the routing of the quantum channelin the mesh quantum network. The entanglement generation rate is alsoreferred to the generation rate, an entanglement consumption rate, aquantum channel rate, or an entangled bandwidth in the disclosure.

Two quantum computers at two remote end points can communicate through aquantum channel, which would require to determine a minimum entanglementconsumption rate 1/T_(c) (qubit/sec) or entangled bandwidth and aminimum acceptable fidelity F_(m) for a specific quantum computingapplication. The entanglement consumption rate can be assimilated to atransfer bandwidth.

Given as described above, it is now clear that the most appropriate pathacross the mesh quantum network is not simply associated with the numberof hops or the length of the path. The selection of the appropriate pathneeds to be weighted with the technology used in each quantum node ofthe quantum network in order to deliver necessary quantum channel ratewith the appropriate fidelity and coherence time or lifetime for eachquantum computing application.

The disclosure provides a routing protocol or algorithm to select a pathacross a mesh quantum network based upon the fidelity and coherence timeor lifetime. In an analogue way, the path across the mesh quantumnetwork may have an entanglement generation rate 1/T_(p) (i.e. entangledbandwidth), and a path fidelity F_(p)(t) with a fidelity time constantT_(F) that characterizes a fidelity evolution over time, whereF_(p)(t)=F_(p)e^(−t/T) _(F), where F_(p) is an initial constant for thefidelity. Alternative functions can also be used to characterize thefidelity evolution over time. To support a specific quantum computingapplication, the following Equations (1) and (2) need to be satisfied:

1/T _(p)>1/T _(c)  Equation (1)

and

F _(m) <F _(p)(T _(c))=F _(p) e ^(−T) _(c) ^(/T) _(F)  Equation (2)

where F_(m) is a minimum path fidelity and 1/T_(c) is a minimumentanglement generation rate for a quantum computing application.

The routing protocol can either work in a centralized approach or in adistributed approach. However, in order to implement an appropriaterouting protocol, one needs to be aware of the specific constraintsposed by the quantum technology behind the quantum communication.

FIG. 6 illustrates selecting an appropriate routing path across a meshquantum network, in accordance with some aspects of the disclosedtechnology. As illustrated, a quantum network 600 includes a pluralityof quantum nodes 101A-101G, connected by links 604A-J between twoneighboring nodes. For example, link 604A connects quantum nodes 101Aand 101B. Quantum node 101A is in a communication with an end user 608Aat one end point or an end node. Quantum node 101G is in a communicationwith another end user 608G at another end point or another end note. Thecommunication may be telecommunication using visible or microwaves. Incontrast, quantum communication may go through photons.

The network 600 has a minimum fidelity Fm and a minimum entanglementgeneration rate 1/T, for a specific quantum computing application. As anexample, three possible paths 606A-606C are illustrated. A first path606A includes two links 6041 and 604J. A second path 606B includes fourlinks 604B, 604D, 604C, and 604H. A third path 606C includes six links604A, 604K, 604C, 604D, 604F, and 604G.

The path 606A has a path generation rate 1/T_(F) ^(a), and a pathfidelity F_(p) ^(a). Each link of the path 606A has a generation rate1/T_(F) ^(a1), a fidelity F_(p) ^(a1), 1/T_(F) ^(a2), F_(p) ^(a2),1/T_(F) ^(a3), F_(p) ^(a3) . . . . Likewise, the path 606B has a pathgeneration rate 1/T_(F) ^(b), and a path fidelity F_(p) ^(b). Each linkof the path 606B has a generation rate 1/T_(F) ^(b1), a fidelity F_(p)^(b1), 1/T_(F) ^(b2), F_(p) ^(b2), 1/T_(F) ^(b3), F_(p) ^(b3) . . . .The path 606C has a path generation rate 1/T_(F) ^(c), and a pathfidelity F_(p) ^(c). Each link of the path 606C has a generation rate1/T_(F) ^(c1), a fidelity F_(p) ^(c1), 1/T_(F) ^(c2), F_(p) ^(c2),1/T_(F) ^(c3), F_(p) ^(c3) . . . where the numbers 1, 2, 3 representslink 1, link 2, and link 3, respectively.

Each link or path can handle fidelity and entanglement generation rateas an ensemble of multiple solutions (F_(p1), 1/T_(p1); F_(p2),1/T_(p2); F_(p3), 1/T_(p3); . . . ), where the numbers 1, 2, and 3represent path 1, path 2, path 3, respectively.

The quantum path may be selected based upon the fidelityF_(p)(t)=F_(p)e^(−t/T) _(F) greater than the minimum F_(m) for a quantumcomputing application, wherein F_(p) is an initial fidelity, and T_(F)is a fidelity time constant, and also based upon an entanglementgeneration rate 1/T_(p) greater than 1/T_(c). The generation rate andthe fidelity of the selected quantum path must satisfy Equations (1) and(2). As an example, all the links of the path 606B may satisfy Equations(1) and (2), while not all the links of the path 606A or 606C satisfyEquations (1) and (2). As such, the path 606B may be selected as therouting path or communication path from the end user 608A to the otherend user 608G. The links of the path 606B are used to ultimatelyposition a pair of entanglement particles with one particle at a sourcenode and the other particle of the entangled pair at the destinationnode. The entanglement of the link is an intermediate state. Whenentanglement swapping is performed, the entanglement between the initialpair of particles is consumed (or destroyed) and the entanglement statustransferred to a different pair of particles. This process can acrossmultiple links in a path until the respective particles of a pair ofentangled particles are properly positioned.

Calculation of the parameters for each path has some complexities,because the calculation needs to combine similar information for eachquantum link of the quantum network (e.g. entanglement generation rate,and fidelity), with the quantum memory coherence time of each node, withthe latency to transfer classical information on each quantum link andacross the path. Also, the path fidelity is affected by the fidelity ofeach Bell state entangled pair and also by gate operations includingentanglement swapping. A higher fidelity can also be achieved using thepurification procedure at link, multi-link or on the entire path,sacrificing the entanglement generation rate for each Bell stateentangled pair across the quantum network. For example, reducing theentanglement generation rate may increase the fidelity. The calculationof the entanglement generation rate and the fidelity may use knowniteration methods.

The latency for a classical communication across multiple links from endto end, as in entanglement swapping or purification cases, may be lowerthan the sum of the latency of each link, because the classicalcommunication can use a shorter path across the network.

A database including parameters (e.g. F_(p1), 1/T_(p1); F_(p2),1/T_(p2); F_(p3), 1/T_(p3); . . . ) and/or (1/T_(F) ^(a1), F_(p) ^(a1),F_(p) ^(a2), 1/T_(F) ^(a2), F_(p) ^(a2), 1/T_(F) ^(a3), F_(p) ^(a3))needs to be continuously updated, because updated parameters can beaffected by other quantum applications running across the same network.Different from the classical network, but similar to traffic engineerednetworks, the database accounts for all the entangled bandwidths orentanglement consumption rates of all the active applications or all therunning applications.

Each of the plurality of quantum nodes has a respective fidelity and arespective coherence decay time in the mesh quantum network. Theparameters including fidelity and generation rate are analyzed for eachnode in the database to yield a determination of a path fidelity with apath coherence decay time and a path generation rate.

In some variations, a quantum communication path may be selected from asource node to a destination node based upon the path fidelityF_(p)(t)=F_(p)e^(−t/T) _(F) greater than the minimum fidelity F_(m) forthe quantum computing application and the entanglement generation rate1/T_(p) greater than the minimum entanglement generation rate 1/T_(c).

In some variations, the quantum communication path can be routed throughthe first quantum link from the first quantum node to the second quantumnode by using the controller, and then routed through the second quantumlink from the second quantum node to the third quantum node by using thecontroller.

In some variations, a quantum communication path may be selected basedupon a highest margin of the path fidelity for a quantum communicationpath.

In some variations, a quantum communication path may be selected basedupon a lowest margin of the path fidelity for a quantum communicationpath.

In some variations, a quantum communication path may be selected basedupon a highest margin of the entanglement generation rate for a quantumcommunication path.

In some variations, a quantum communication path may be selected basedupon a lowest margin of the entanglement generation rate for a quantumcommunication path.

In some variations, the protocol may maximize margins in theentanglement generation rate and/or the path fidelity to identify anappropriate path between two end points to guarantee the operations of aspecific quantum computing application.

In some variations, the protocol may minimize margins in theentanglement generation rate and/or the path fidelity to identify anappropriate path between two end points to guarantee the operations of aspecific quantum computing application.

In some variations, the protocol may maximize one margin in theentanglement generation rate (or the path fidelity) and minimize anothermargin in the path fidelity (or the entanglement generation rate) toidentify an appropriate path between two end points to guarantee theoperations of a specific quantum computing application.

In some variations, the routing protocol for selection of the path canbe a distributed one that builds the path by hops from one node toanother node.

In some variations, the routing protocol can also be a centralized onethat runs in a personal consumption expenditure (POE) link applicationthat collects information from each node of the network.

In some aspects, the entanglement generation rate can split acrossmultiple quantum paths, i.e. a total entanglement consumption rate or atotal entangled bandwidth can be split across multiple paths adoptingstrategy 1 or 2 for the selection of each path.

FIG. 7 illustrates splitting a quantum path across a mesh quantumnetwork, in accordance with some aspects of the disclosed technology. Asshown in FIG. 7 , a network 700 may include a plurality of quantum nodes101A-101G, which are connected by links 704A-J between two neighboringnodes. The network 700 includes two paths, i.e. Path 706 b and Path 706c. The quantum split path rules are provided in Equations (3) and (4):

1/T _(c)<1/T _(p) ^(b)+1/T _(p) ^(c)  Equation (3)

F _(m) <F _(p) ^(b)(T _(c)),F _(p) ^(c)(T _(c))  Equation (4)

where T_(F) ^(b), F_(p) ^(b), 1/T_(p) ^(b) are an initial time constant,a fidelity, and an entanglement generation rate for Path 706 brespectively, while T_(F) ^(c), F_(p) ^(c), 1/T_(p) ^(c) are an initialtime constant, a fidelity, and an entanglement generation rate for Path706 c, respectively. As shown in Equation (3), the sum of theentanglement generation rate of the Path 706 b and Path 706 c is greaterthan 1/T_(c). The fidelity F_(p) ^(b)(T_(c)) and F_(p) ^(c)(T_(c)) ofeach of Path 706 b and Path 706 c is greater than F_(m).

The network 700 can select quantum links of the quantum communicationpath (e.g. Path 706 b and Path 706 c) from a first end point 101A to asecond end point 101G based upon the path fidelity F_(p)(t) of the firstquantum communication path (e.g. Path 706 b) and the path fidelityF_(p)(t) of the second quantum communication path (e.g. Path 706 c)greater than the minimum F_(m) for the quantum computing application anda combined entanglement generation rate 1/T_(p) of the first quantumcommunication path (e.g. Path 706 b) and the second quantumcommunication path (e.g. Path 706 c) greater than 1/T_(a). The secondquantum communication path (Path 706 c) has a same end point as thefirst quantum communication path (Path 706 b).

FIG. 8 illustrates a combination of a classical communication path and aquantum communication path, in accordance with some aspects of thedisclosed technology. A network 800 includes a plurality of quantumnodes 802A-G and a plurality of links or quantum channels 404(illustrated in dash lines) that connect the plurality of quantum nodes802A-G. Note that a quantum communication path or quantum entanglementswapping path 806A is illustrated from a source quantum node 802A to adestination quantum node 802G. Each of quantum nodes 802A-G includes aprocessor 105 and a quantum memory device 107. The processor 105 of eachof nodes 802A-G is in a communication with a controller 108. The quantumcommunication path or quantum entanglement swapping path 806A includesmultiple quantum links or quantum channels 404.

The network 800 also includes a plurality of classical nodes 808A-G anda plurality of classical links 804A-F (illustrated in solid lines witharrows) that connect the plurality of classical nodes 808A-G. Note thata classical communication path 806B is illustrated from a sourceclassical node 808A to a destination classical node 808G. The pluralityof classical nodes are located at respective locations of the pluralityof quantum nodes 802A-G. Each of classical nodes 808A-G includes aprocessor and a memory device. The processor of each of classical nodes808A-G is also in a communication with the controller 108. Thecontroller 108 may include one or more processors that are configured toexecute a routing algorithm method for the quantum communication pathacross the network 800 including the quantum nodes and classical nodes.The controller 108 may include a memory device. The routing algorithmare instructions that can be stored in the memory device and executed bythe processors. The routing method for the classical path is atraditional network method.

FIG. 9 is a flow chart illustrating steps for selecting a routing pathin a quantum network, in accordance with some aspects of the disclosedtechnology. Although the example method 900 depicts a particularsequence of operations, the sequence may be altered without departingfrom the scope of the present disclosure. For example, some of theoperations depicted may be performed in parallel or in a differentsequence that does not materially affect the function of the method 900.In other examples, different components of an example device or systemthat implements the method 900 may perform functions at substantiallythe same time or in a specific sequence.

According to some examples, the method 900 includes receiving parametersincluding fidelity with coherence decay time and an entanglementgeneration rate for each quantum node in a mesh quantum network by acontroller, the controller being configured to communicate with eachquantum node of a plurality of quantum nodes in the mesh quantumnetwork, each quantum node including a quantum memory and a processor atblock 910. In some embodiments, the processor is a classical processor.For example, the controller 108 illustrated in FIG. 1A may receiveparameters including fidelity with coherence decay time and anentanglement generation rate for each quantum node in a mesh quantumnetwork by a controller, the controller be configured to communicatewith each quantum node of a plurality of quantum nodes in the meshquantum network, each quantum node including a quantum memory and aprocessor.

According to some examples, the method includes analyzing the fidelitywith coherence decay time and the entanglement generation rate betweenat least one pair of quantum nodes to yield a determination of a pathfidelity with a path coherence decay time and a path entanglementgeneration rate at block 920. For example, the controller 108illustrated in FIG. 1A may analyze the fidelity with coherence decaytime and the entanglement generation rate between at least one pair ofquantum nodes to yield a determination of a path fidelity with a pathcoherence decay time and a path entanglement generation rate.

According to some examples, the method includes based on thedetermination, selecting, through the mesh quantum network, a quantumcommunication path from a first end point or a source node to a secondend point or a destination node at block 930. For example, thecontroller 108 illustrated in FIG. 1A may select, through the meshquantum network, a quantum communication path from a first end point ora source node to a second end point or a destination node, based on thedetermination.

FIG. 10 shows an example of computing system 1000, which can be forexample any computing device making up the controller 108, or anycomponent thereof in which the components of the system are incommunication with each other using connection 1005. Connection 1005 canbe a physical connection via a bus, or a direct connection intoprocessor 1010, such as in a chipset architecture. Connection 1005 canalso be a virtual connection, networked connection, or logicalconnection.

In some embodiments, computing system 1000 is a distributed system inwhich the functions described in this disclosure can be distributedwithin a datacenter, multiple data centers, a peer network, etc. In someembodiments, one or more of the described system components representsmany such components each performing some or all of the function forwhich the component is described. In some embodiments, the componentscan be physical or virtual devices.

Example system 1000 includes at least one processing unit (CPU orprocessor) 1010 and connection 1005 that couples various systemcomponents including system memory 1015, such as read-only memory (ROM)1020 and random access memory (RAM) 1025 to processor 1010. Computingsystem 1000 can include a cache of high-speed memory 1012 connecteddirectly with, in close proximity to, or integrated as part of processor1010.

Processor 1010 can include any general purpose processor and a hardwareservice or software service, such as services 1032, 1034, and 1036stored in storage device 1030, configured to control processor 1010 aswell as a special-purpose processor where software instructions areincorporated into the actual processor design. Processor 1010 mayessentially be a completely self-contained computing system, containingmultiple cores or processors, a bus, memory controller, cache, etc. Amulti-core processor may be symmetric or asymmetric.

To enable user interaction, computing system 1000 includes an inputdevice 1045, which can represent any number of input mechanisms, such asa microphone for speech, a touch-sensitive screen for gesture orgraphical input, keyboard, mouse, motion input, speech, etc. Computingsystem 1000 can also include output device 1035, which can be one ormore of a number of output mechanisms known to those of skill in theart. In some instances, multimodal systems can enable a user to providemultiple types of input/output to communicate with computing system1000. Computing system 1000 can include communications interface 1040,which can generally govern and manage the user input and system output.There is no restriction on operating on any particular hardwarearrangement, and therefore the basic features here may easily besubstituted for improved hardware or firmware arrangements as they aredeveloped.

Storage device 1030 can be a non-volatile memory device and can be ahard disk or other types of computer readable media which can store datathat are accessible by a computer, such as magnetic cassettes, flashmemory cards, solid state memory devices, digital versatile disks,cartridges, random access memories (RAMs), read-only memory (ROM),and/or some combination of these devices.

The storage device 1030 can include software services, servers,services, etc., that when the code that defines such software isexecuted by the processor 1010, it causes the system to perform afunction. In some embodiments, a hardware service that performs aparticular function can include the software component stored in acomputer-readable medium in connection with the necessary hardwarecomponents, such as processor 1010, connection 1005, output device 1035,etc., to carry out the function.

For clarity of explanation, in some instances, the present technologymay be presented as including individual functional blocks includingfunctional blocks comprising devices, device components, steps orroutines in a method embodied in software, or combinations of hardwareand software.

Any of the steps, operations, functions, or processes described hereinmay be performed or implemented by a combination of hardware andsoftware services or services, alone or in combination with otherdevices. In some embodiments, a service can be software that resides inmemory of a client device and/or one or more servers of a contentmanagement system and perform one or more functions when a processorexecutes the software associated with the service. In some embodiments,a service is a program or a collection of programs that carry out aspecific function. In some embodiments, a service can be considered aserver. The memory can be a non-transitory computer-readable medium.

In some embodiments, the computer-readable storage devices, mediums, andmemories can include a cable or wireless signal containing a bit streamand the like. However, when mentioned, non-transitory computer-readablestorage media expressly exclude media such as energy, carrier signals,electromagnetic waves, and signals per se.

Methods according to the above-described examples can be implementedusing computer-executable instructions that are stored or otherwiseavailable from computer-readable media. Such instructions can comprise,for example, instructions and data which cause or otherwise configure ageneral purpose computer, special purpose computer, or special purposeprocessing device to perform a certain function or group of functions.Portions of computer resources used can be accessible over a network.The executable computer instructions may be, for example, binaries,intermediate format instructions such as assembly language, firmware, orsource code. Examples of computer-readable media that may be used tostore instructions, information used, and/or information created duringmethods according to described examples include magnetic or opticaldisks, solid-state memory devices, flash memory, USB devices providedwith non-volatile memory, networked storage devices, and so on.

Devices implementing methods according to these disclosures can comprisehardware, firmware and/or software, and can take any of a variety ofform factors. Typical examples of such form factors include servers,laptops, smartphones, small form factor personal computers, personaldigital assistants, and so on. The functionality described herein alsocan be embodied in peripherals or add-in cards. Such functionality canalso be implemented on a circuit board among different chips ordifferent processes executing in a single device, by way of furtherexample.

The instructions, media for conveying such instructions, computingresources for executing them, and other structures for supporting suchcomputing resources are means for providing the functions described inthese disclosures.

Any ranges cited herein are inclusive. The terms “substantially” and“about” used throughout this Specification are used to describe andaccount for small fluctuations. For example, they can refer to less thanor equal to ±5%, such as less than or equal to ±2%, such as less than orequal to ±1%, such as less than or equal to ±0.5%, such as less than orequal to ±0.2%, such as less than or equal to ±0.1%, such as less thanor equal to ±0.05%.

Having described several embodiments, it will be recognized by thoseskilled in the art that various modifications, alternativeconstructions, and equivalents may be used without departing from thespirit of the invention. Additionally, a number of well-known processesand elements have not been described in order to avoid unnecessarilyobscuring the invention. Accordingly, the above description should notbe taken as limiting the scope of the invention.

Those skilled in the art will appreciate that the presently disclosedembodiments teach by way of example and not by limitation. Therefore,the matter contained in the above description or shown in theaccompanying drawings should be interpreted as illustrative and not in alimiting sense. The following claims are intended to cover all genericand specific features described herein, as well as all statements of thescope of the method and system, which, as a matter of language, might besaid to fall therebetween.

What is claimed is:
 1. A method for routing in a quantum network, themethod comprising: receiving parameters comprising a fidelity withcoherence decay time and an entanglement generation rate for eachquantum node in a mesh quantum network by a controller, the controllerbeing configured to communicate with each quantum node of a plurality ofquantum nodes in the mesh quantum network, each quantum node comprisinga quantum memory and a processor; analyzing the fidelity with coherencedecay time and the entanglement generation rate to yield a determinationof a path fidelity with a path coherence decay time and a pathentanglement generation rate between at least one pair of quantum nodesof the plurality of quantum nodes; and based on the determination,selecting, through the mesh quantum network, a first quantumcommunication path from a source node to a destination node.
 2. Themethod of claim 1, wherein the determination comprises a minimum pathfidelity F_(m) and a minimum entanglement generation rate 1/T_(c) for aquantum computing application.
 3. The method of claim 2, whereinselecting the first quantum communication path is based upon a pathfidelity F_(p)(t)=F_(p)e^(−t/T) _(F) of the first quantum communicationpath being greater than the minimum path fidelity F_(m) for a quantumcomputing application, wherein F_(p) is an initial fidelity, and T_(F)is a fidelity time constant.
 4. The method of claim 3, wherein theselecting the first quantum communication path is based upon a pathentanglement generation rate 1/T_(p) greater than 1/T_(c).
 5. The methodof claim 3, wherein the selecting the first communication path furthercomprises selecting a second quantum communication path from the sourcenode to the destination node based upon the path fidelity F_(p)(t) ofthe first quantum communication path and a second path fidelity F_(p)(t)of the second quantum communication path being greater than the minimumpath fidelity F_(m) for the quantum computing application and a combinedentanglement generation rate 1/T_(p) of the first quantum communicationpath and the second quantum communication path being greater than1/T_(c).
 6. The method of claim 5, wherein the second quantumcommunication path has a same end point as the first quantumcommunication path.
 7. The method of claim 1, wherein the networkfurther comprises a classical communication path between a plurality ofclassical nodes, where each of the plurality of classical nodes islocated at a respective location of each of the plurality of quantumnodes, each classical node comprising a classical processor and a memorydevice.
 8. The method of claim 1, wherein the first quantumcommunication path between the source node and the destination nodecomprises at least one quantum link.
 9. The method of claim 1, furthercomprising teleporting by transferring a qubit is based upon a pair ofentangled particles, in which a first entangled particle of the pair ofentangled particles is at the source node and a second entangledparticle of the pair of entangled particles is at the destination node,after completing quantum swapping that extends a distance between thefirst entangled particle and the second entangled particle usingentanglement swapping repeaters from the source node to the destinationnode.
 10. The method of claim 1, wherein the selecting the first quantumcommunication path is based upon a highest margin of the fidelity for aquantum communication path.
 11. The method of claim 1, wherein theselecting the first quantum communication path is based upon a lowestmargin of the fidelity for a quantum communication path.
 12. The methodof claim 1, wherein the selecting the first quantum communication pathis based upon a highest margin of the entanglement generation rate for aquantum communication path.
 13. The method of claim 1, wherein theselecting the first quantum communication path is based upon a lowestmargin of the entanglement generation rate for a quantum communicationpath.
 14. The method of claim 1, wherein each of the plurality ofquantum nodes comprises one particle of a first pair of entangledparticles and one particle of a second pair of entangled particles. 15.A controller comprising: one or more processors; and a non-transitorycomputer readable medium comprising instructions stored therein, theinstructions, when executed by the one or more processors, cause theprocessors perform operations comprising: receiving parameterscomprising a fidelity with coherence decay time and an entanglementgeneration rate for each quantum node in a mesh quantum network, thecontroller being configured to communicate with each quantum node of aplurality of quantum nodes in the mesh quantum network, each quantumnode comprising a quantum memory and a processor; analyzing the fidelitywith coherence decay time and the entanglement generation rate to yielda determination of a path fidelity with a path coherence decay time anda path entanglement generation rate between at least one pair of quantumnodes; and based on the determination, selecting, through the meshquantum network, a quantum communication path from a source node to adestination node.
 16. The controller of claim 15, wherein thedetermination comprises a minimum path fidelity F_(m) and a minimumentanglement generation rate 1/T_(c) for a quantum computingapplication.
 17. The controller of claim 16, wherein the selecting thequantum communication path is based upon a path fidelityF_(p)(t)=F_(p)e^(−t/T) _(F) greater than the minimum F_(m) for a quantumcomputing application, wherein F_(p) is an initial fidelity, and T_(F)is a fidelity time constant.
 18. The controller of claim 16, wherein theselecting the quantum communication path is based upon a pathentanglement generation rate 1/T_(p) greater than 1/T.
 19. Anon-transitory computer readable medium comprising instructions, theinstructions, when executed by a computing system, cause the computingsystem to perform operations comprising: receiving parameters comprisinga fidelity with coherence decay time and an entanglement generation ratefor each quantum node in a mesh quantum network, the computing systembeing configured to communicate with each quantum node of a plurality ofquantum nodes in the mesh quantum network, each quantum node comprisinga quantum memory and a processor; analyzing the fidelity with coherencedecay time and the entanglement generation rate to yield a determinationof a path fidelity with a path coherence decay time and a pathentanglement generation rate between at least one pair of quantum nodes;and based on the determination, selecting, through the mesh quantumnetwork, a quantum communication path from a source node to adestination node.
 20. The non-transitory computer readable medium ofclaim 19, wherein the determination comprises a minimum path fidelityF_(m) and a minimum entanglement generation rate 1/T_(c) for a quantumcomputing application, wherein the selecting of the quantumcommunication path is based upon a path entanglement generation rate1/T_(p) greater than 1/T_(c).